Any landowner or operator may file a petition with the board of adjustment alleging that there are great practical difficulties or unnecessary hardships in the way of his carrying out upon his lands the strict letter of the land-use regulations prescribed by ordinance approved by the commissioners, and praying the board to authorize a variance from the terms of the land-use regulations in the application of such regulations to the lands owned or operated by the petitioner. Copies of such petition shall be served by the petitioner upon the chairman of the commissioners of the district within which his lands are located and upon the chairman of the State Soil and Water Conservation Committee. The board of adjustment shall fix a time for the hearing of the petition and cause due notice of such hearing to be given. The commissioners of the district and the State Soil and Water Conservation Committee shall have the right to appear and be heard at such hearing. Any owner or operator of lands lying within the district who shall object to the authorizing of the variance prayed for may intervene and become a party to the proceedings. Any party to the hearing before the board may appear in person, by agent, or by attorney. If, upon the facts presented at such hearing, the board shall determine that there are great practical difficulties or unnecessary hardship in the way of applying the strict letter of any of the land-use regulations upon the lands of the petitioner, it shall make and record such determination and shall make and record findings of fact as to the specific conditions which establish such great practical difficulties or unnecessary hardship. Upon the basis of such findings and determination, the board shall have power by order to authorize such variance from the terms of land-use regulations in their application to the lands of the petitioner, as will relieve such great practical difficulties or unnecessary hardship and will not be contrary to the public interest, and such that the spirit of the land-use regulations shall be observed, the public health, safety, and welfare secured, and substantial justice done.